The invention relates to a wavelength-tuning, phase-shifting interferometry.
Interferometric optical techniques are widely used to measure optical thickness, flatness, and other geometric and refractive index properties of precision optical components such as glass substrates used in lithographic photomasks.
For example, to measure the surface profile of a measurement surface, one can use an interferometer to combine a measurement wavefront reflected from the measurement surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined measurement and reference wavefronts caused by variations in the profile of the measurement surface relative to the reference surface. Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences and the corresponding profile of the measurement surface.
With PSI, the optical interference pattern is recorded for each of multiple phase-shifts between the reference and measurement wavefronts to produce a series of optical interference patterns that span a full cycle of optical interference (e.g., from constructive, to destructive, and back to constructive interference). The optical interference patterns define a series of intensity values for each spatial location of the pattern, wherein each series of intensity values has a sinusoidal dependence on the phase-shifts with a phase-offset equal to the phase difference between the combined measurement and reference wavefronts for that spatial location. Using numerical techniques known in the art, the phase-offset for each spatial location is extracted from the sinusoidal dependence of the intensity values to provide a profile of the measurement surface relative the reference surface. Such numerical techniques are generally referred to as phase-shifting algorithms.
The phase-shifts in PSI can be produced by changing the optical path length from the measurement surface to the interferometer relative to the optical path length from the reference surface to the interferometer. For example, the reference surface can be moved relative to the measurement surface. Alternatively, the phase-shifts can be introduced for a constant, non-zero optical path difference by changing the wavelength of the measurement and reference wavefronts. The latter application is known as wavelength tuning PSI and is described, e.g., in U.S. Pat. No. 4,594,003 to G. E. Sommargren.
Unfortunately, PSI measurements can be complicated by spurious reflections from other surfaces of the measurement object because they too contribute to the optical interference. In such cases, the net optical interference image is a superposition of multiple interference pattern s produced by pairs of wavefronts reflected from the multiple surfaces of the measurement object and the reference surface.
The invention features a method for extracting selected interference data from overlapping optical interference patterns arising from spurious reflections. The method takes advantage of the fact that for each interference pattern, a change in optical wavelength induces a phase-shift that is substantially linearly proportional to the optical path difference (OPD) corresponding to the two wavefronts giving rise to the interference pattern. In other words, the intensity profile of each interference pattern has a sinusoidal dependence on wavelength, and that sinusoidal dependence has a phase-shifting frequency proportional to the OPD for that interference pattern. To extract the phase-information of the interference pattern of interest, the method employs a phase-shifting algorithm that is more sensitive to the phase-shifting frequency of the selected interference pattern than to those of the other interference patterns in the image.
In general, in one aspect, the invention features a method for interferometrically profiling a measurement object having multiple reflective surfaces. The method includes: positioning the measurement object within an unequal path length interferometer (e.g., a Fizeau interferometer) employing a tunable coherent light source; recording an optical interference image for each of multiple wavelengths of the light source, each image including a superposition of multiple interference patterns produced by pairs of wavefronts reflected from the multiple surfaces of the measurement object and a reference surface; and extracting phases of a selected one of the interference patterns from the recorded images by using a phase-shifting algorithm that is more sensitive (e.g., at least ten times more sensitive) to a wavelength-dependent variation in the recorded images caused by the selected interference pattern than to wavelength-dependent variations in the recorded images caused by the other interference patterns.
Embodiments of the profiling method can include any of the following features. The phase-shifting algorithm can include a phase calculation equal to an arctangent of a ratio, the numerator and denominator of the ratio being weighted sums of intensity values of the recorded images at each spatial coordinate. More specifically, the phase-shifting algorithm can be a Fourier-series phase-shifting algorithm. The multiple wavelengths can be spaced from one another to impart substantially equal phase-shifts between the selected interference patterns in consecutive images. Furthermore, the multiple wavelengths can be spaced from one another to impart an absolute phase-shift of less than 2xcfx80 between the selected interference patterns in consecutive images. Alternatively, the multiple wavelengths can be spaced from one another to impart an absolute phase-shift of greater than 2xcfx80 between the selected interference patterns in consecutive images (i.e., sub-Nyquist sampling).
In general, in another aspect, the invention features a method for interferometrically profiling a measurement object having multiple reflective surfaces. The method includes: positioning the measurement object within an unequal path length interferometer employing a tunable coherent light source; recording an optical interference image for each of multiple wavelengths of the light source, each image including a superposition of multiple interference patterns produced by pairs of wavefronts reflected from the multiple surfaces of the measurement object and a reference surface; and extracting phases of a selected one of the interference patterns from the recorded images by using a Fourier-series phase-shifting algorithm.
The Fourier-series phase-shifting algorithm can include a phase calculation equal to an arctangent of a ratio, the numerator and denominator of the ratio being weighted sums of intensity values of the recorded optical interference patterns at each spatial coordinate. For example, the phase calculation can corresponds to:       tan    ⁡          (      θ      )        =                                                                        -                3                            ⁢                              (                                                      g                    0                                    -                                      g                    12                                                  )                                      -                          4              ⁢                              (                                                      g                    1                                    -                                      g                    11                                                  )                                      +                          12              ⁢                              (                                                      g                    3                                    -                                      g                    9                                                  )                                      +                          21              ⁢                              (                                                      g                    4                                    -                                      g                    8                                                  )                                      +                          16              ⁢                              (                                                      g                    5                                    -                                      g                    7                                                  )                                                                                  -          4                ⁢                  (                                    g              1                        +                          g              11                                )                    -              12        ⁢                  (                                    g              2                        +                          g              3                        +                          g              9                        +                          g              10                                )                    +              16        ⁢                  (                                    g              5                        +                          g              7                                )                    +              24        ⁢                  g          6                    
where for each spatial coordinate, xcex8 is the phase extracted by the algorithm and gj is the intensity value of the xe2x80x9cjthxe2x80x9d image, and where the wavelength shift xcex94xcex between consecutive patterns corresponds to a phase shift substantially equal to xcfx80/4 for the selected interference pattern.
In general, in a further aspect, the invention features a system for profiling a measurement object having multiple reflective surfaces including a tunable coherent light source, an unequal length interferometer (e.g., a Fizeau interferometer), a detector, and a system controller. The light source is configured to generate light at any one of multiple wavelengths. The interferometer includes a mount configured to position a selected one of the reflective surfaces of the measurement object at a non-zero distance Z from the zero optical path difference (OPD) position of the interferometer. The distance Z is less than about nT/2, nT being the smallest optical distance between two of the multiple reflective surfaces of the measurement object. The interferometer is also configured to receive the light from light source and generate an optical interference image including a superposition of multiple interference patterns produced by pairs of wavefronts reflected from the multiple surfaces of the measurement object and a reference surface. The detector is configured to record the optical interference image generated by the interferometer. The system controller is connected to the light source and the detector. During operation it causes the light source to generate light at each of the multiple wavelengths, causes the detector to record the image for each of the multiple wavelengths of the light source, and implements a phase-shifting algorithm to determine phases of a selected one of the interference patterns from the recorded images.
Embodiments of the profiling system can have any of the following features. The distance Z can satisfy the expression nT/2xe2x89xa7Zxe2x89xa7nT/5, for example Z can be equal to about nT/3. The phase-shifting algorithm implemented by the controller can be more sensitive to a wavelength-dependent variation in the recorded images caused by the selected interference pattern than to wavelength-dependent variations in the recorded images caused by the other interference patterns. The phase-shifting algorithm implemented by the controller can be a Fourier-series phase-shifting algorithm.
In general, in a further aspect, the invention features a system for profiling a measurement object having multiple reflective surfaces including: including a tunable coherent light source, an unequal length interferometer (e.g., a Fizeau interferometer), a detector, and a system controller. The tunable coherent light source is configured to generate light at any one of multiple wavelengths spanning a range greater than or equal to about xcex2/nT, where xcex is an intermediate one of the multiple wavelengths and nT is the smallest optical distance between two of the multiple reflective surfaces of the measurement object. The interferometer is configured to support the measurement object, receive the light from light source, and generate an optical interference image including a superposition of multiple interference patterns produced by pairs of wavefronts reflected from the multiple surfaces of the measurement object and a reference surface. The detector is configured to record the optical interference image generated by the interferometer. The system controller is connected to the light source and the detector. During operation it causes the light source to generate light at each of the multiple wavelengths, causes the detector to record the optical interference image for each of the multiple wavelengths of the light source, and implements a phase-shifting algorithm to determine phases of a selected one of the interference patterns from the recorded images.
Embodiments of the profiling system can include any of the following features. The wavelengths can span a range greater than or equal to about 3xcex2/2 nT, e.g., about 5xcex2/2 nT. The tunable coherent source can include a laser diode and a driver, which during operation adjusts the current to the laser diode to vary wavelength output of the laser diode. The phase-shifting algorithm implemented by the controller can be more sensitive to a wavelength-dependent variation in the recorded images caused by the selected interference pattern than to wavelength-dependent variations in the recorded images caused by the other interference patterns. The phase-shifting algorithm implemented by the controller can be a Fourier-series phase-shifting algorithm.
Embodiments of the invention have many advantages. For example, a selected reflective surface of a measurement object can be profiled even though other surfaces produce spurious reflections that complicate the optical interference image. As a result, precision optical substrates such as glass flats can be profiled without coating any of their surfaces. Moreover, the profiling measurements can be as fast and robust as in measurement involving no such spurious reflections. In addition to measuring the topography of a selected surface of the measurement object, the optical profile of the measurement object including refractive index inhomogeneities can also be measured.
Other aspects, advantages, and features will be apparent from the following detailed description and from the claims.